całka
: 25 wrz 2007, o 13:07
wie może ktoś jak obliczyć tą całki?
\(\displaystyle{ \int_1^4\frac{x^2+2}{x^2+6x+10}dx}\)
\(\displaystyle{ \int_1^4\frac{x^2+2}{x^2+6x+10}dx}\)
\(\displaystyle{ \int\frac{x^2+2}{x^2+6x+10}dx=\int\frac{x^2+6x+10}{x^2+6x+10}dx- t\frac{6x+8}{x^2+6x+10}dx=\int{dx}-\int\frac{3(2x+6)-10}{x^2+6x+10}dx= x-3\int\frac{2x+6}{x^2+6x+10}dx+10\int\frac{dx}{(x+3)^2+1}=}\)
\(\displaystyle{ x-3\ln(x^2+6x+10)+ 10arc\tan(x+3)+C}\)